Provide two different examples of how research uses hypothesis testing, and describe the criteria for rejecting the null hypothesis.
Topic 3 DQ 1
Provide two different examples of how research uses hypothesis testing, and describe the criteria for rejecting the null hypothesis. Discuss why this is important in your practice and with patient interactions.
Topic 3 DQ 2
Expert Answer and Explanation
Topic 3 DQ 1: Hypothesis Testing
The aspect of hypothesis testing refers to the process of creating inferences or otherwise referred to as educated guesses concerning a specific research parameter. Hypothesis testing can be conducted either through the use of uncontrolled observational study or statistics and sample data (Mellenbergh, 2019). Prior to testing a hypothesis, it is essential to come up with the degree of statistical significance in the hypothesis since a researcher cannot be 100 percent on the educated guess.
An example of the use of hypothesis testing is in determining the prevalence of common cold in children who take vitamin C. The null hypothesis would state that the prevalence of flu in children who take vitamin C is similar to those who don’t take vitamin C. the alternative hypothesis would be that children with the uptake of vitamin C have a reduced prevalence of flu in flu seasons.
Another example would be research to identify if therapy is more effective than a placebo. In order to reject the null hypothesis, a redetermined number of subjects among the hypothesis test have to prove the alternative hypothesis. The proof will then overturn the original null hypothesis, which will then be rejected.
Hypothesis testing is an important aspect of statistics and research as it provides a basis for understanding whether something actually occurred or if certain groups or sets of data are different from each other (Dubois, 2017). Hypothesis testing also helps in identifying if an aspect of the research has more positive effects or if a variable can predict another to form a basis for defining a conclusion. With the help of the calculated probability (p-value), one can easily determine the inclination of the research based on either the null hypothesis of the alternative hypothesis.
Dubois, S. (2017). The Importance of Hypothesis Testing. (2020). Retrieved 18 May 2020, from https://sciencing.com/the-importance-of-hypothesis-testing-12750921.html
Mellenbergh, G. J. (2019). Null Hypothesis Testing. In Counteracting Methodological Errors in Behavioral Research (pp. 179-218). Springer, Cham. https://link.springer.com/book/10.1007/978-3-030-12272-0
Topic 3 DQ 2: Hypothesis Testing and Confidence Intervals
Hypothesis tests and confidence intervals are related in the sense that they both are inferential methods that are based on an approximated sampling distribution. The hypothesis tests make use of data from a given sample to test the predetermined hypothesis (Sacha & Panagiotakos, 2016). On the other hand, confidence intervals make use of data from the sample to provide an estimate of the population parameter. In this manner, it is evident that the simulation methods that are used in the construction of the bootstrap distribution, as well as the randomization distributions, are identical.
Confidence intervals are made up of a range of reasonable estimations concerning population parameters. For instance, a two-tailed confidence interval is applied in a two-tailed hypothesis testing. In health care research, a confidence level of 95 percent is mostly used. The level indicates the significance of health research with regards to being precise and accurate with health care data (Hazra, 2017).
For instance, while conducting research on the effect of therapy or medication on patients with mental health conditions. The calculation of the p-value will allow the researcher to achieve the results of the null hypothesis. With a low p-value, a researcher is able to comprehend that there is stronger support for the alternative hypothesis.
In the workplace setting, research can be conducted on the impacts of evidence-based practice on patient outcomes. Hypothesis testing will facilitate the identification of educated guesses, while the confidence interval will provide a basis for the statistical confidence level that will be used in the research (Sacha & Panagiotakos, 2016). The research will then be used to provide a recommendation for the viability of the EBP.
Hazra A. (2017). Using the confidence interval confidently. Journal of thoracic disease, 9(10), 4125–4130. https://doi.org/10.21037/jtd.2017.09.14
Sacha, V., & Panagiotakos, D. B. (2016). Insights in Hypothesis Testing and Making Decisions in Biomedical Research. The open cardiovascular medicine journal, 10, 196–200. https://doi.org/10.2174/1874192401610010196
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Null hypothesis formula
The null hypothesis is typically denoted as H0 and represents the default assumption or statement of no effect, no difference, or no relationship between variables. It is used in statistical hypothesis testing to determine if there is enough evidence to reject or accept the null hypothesis.
There is no one specific formula for the null hypothesis, as it will vary depending on the research question and the type of hypothesis being tested. However, it can often be expressed in words as a statement or assertion about the relationship or lack of relationship between variables.
For example, if we are testing whether there is a difference in the mean height between two groups, the null hypothesis might be:
H0: There is no significant difference in the mean height between Group A and Group B.
In statistical notation, the null hypothesis is often written as:
H0: μ1 = μ2
where μ1 and μ2 represent the population means for Group A and Group B, respectively.
Note that the null hypothesis always assumes equality, and the alternative hypothesis (Ha) is the opposite of the null hypothesis, assuming inequality or a specific direction of effect.
When to reject null hypothesis t test p value
In statistical hypothesis testing using t-tests, the p-value is a measure of the evidence against the null hypothesis. The null hypothesis is rejected when the p-value is less than the significance level (α), which is typically set at 0.05 or 0.01.
Here is a step-by-step guide to interpreting the p-value and deciding whether to reject or fail to reject the null hypothesis in a t-test:
- Formulate the null and alternative hypotheses.
- H0: The population mean is equal to a hypothesized value (e.g. H0: μ = 10)
- Ha: The population mean is not equal to the hypothesized value (e.g. Ha: μ ≠ 10)
- Determine the test statistic (t-value) by computing the ratio of the difference between the sample mean and the hypothesized value to the standard error of the sample mean.
- Calculate the p-value, which is the probability of obtaining a t-value as extreme as or more extreme than the observed t-value, assuming the null hypothesis is true.
- Compare the p-value to the significance level (α). If the p-value is less than α, there is strong evidence against the null hypothesis, and it can be rejected. Conversely, if the p-value is greater than or equal to α, the null hypothesis cannot be rejected.
For example, suppose we want to test whether the mean weight of a sample of 50 people is significantly different from 150 pounds. We perform a two-tailed t-test and obtain a t-value of 2.5 and a p-value of 0.015. We set α = 0.05 as the significance level.
Since the p-value is less than α, we reject the null hypothesis and conclude that the sample mean weight is significantly different from 150 pounds. In other words, there is evidence that the true population mean weight is not equal to 150 pounds.
In summary, the decision to reject or fail to reject the null hypothesis in a t-test depends on the p-value and the significance level. If the p-value is less than or equal to α, the null hypothesis is rejected, and there is evidence of a significant effect or difference. If the p-value is greater than α, the null hypothesis cannot be rejected, and there is insufficient evidence to conclude that there is a significant effect or difference.
Null hypothesis examples
Here are some examples of null hypotheses in different fields:
- Biology: The null hypothesis in a clinical trial might be that a new drug has no effect on a particular medical condition.
H0: The new drug does not significantly reduce the symptoms of the medical condition compared to a placebo.
- Psychology: The null hypothesis in a study on memory might be that there is no difference in recall between two groups of participants.
H0: There is no significant difference in the number of words recalled by participants who studied the words in silence compared to those who studied them while listening to music.
- Education: The null hypothesis in a study on teaching methods might be that there is no difference in student achievement between two different teaching approaches.
H0: There is no significant difference in student test scores between a traditional lecture-based teaching method and an active-learning approach.
- Finance: The null hypothesis in a study on stock returns might be that there is no difference in the average return between two different portfolios.
H0: There is no significant difference in the average annual return between a portfolio of large-cap stocks and a portfolio of small-cap stocks.
- Sociology: The null hypothesis in a study on social attitudes might be that there is no relationship between political ideology and support for a particular policy.
H0: There is no significant correlation between a person’s political ideology and their support for a carbon tax to reduce greenhouse gas emissions.